Receivers often employ equalizers to compensate for signal distortion suffered during signal propagation over a channel. Most equalization methods include estimating the channel characteristics to determine how the channel is distorting a signal. One way to determine that distortion is to send over the channel a signal known by the receiver. The receiver compares the received signal with the known signal, and an estimate of the channel can be computed. One example of a known signal is a simple pulse. In that case, the received signal is called the channel impulse response and corresponds to the transfer function h of the channel. A more sophisticated known signal is a pilot signal that includes for example a known sequence of bits or symbols. The known pilot sequence is compared with the received sequence to determine how much and where the received signal differs from the known sequence. An equalizer can be viewed as filter of sorts that tries to remove the channel distortion from the received signal.
Orthogonal Frequency Domain Multiplexing (OFDM) pertains to a technology that transmits multiple signals simultaneously over a wired or wireless communication medium. Specifically, the data is distributed over a large number of sub-carriers spaced apart at precise frequencies. That spacing provides the orthogonality needed to facilitate demodulation of each frequency.
Wireless-based OFDM receivers may be employed to transmit multiple data streams over a number of parallel flat fading channels. Equalization may be performed in the frequency domain using one-tap digital filters. Channel estimation is performed using known pilot sequences. Pilot signals are transmitted at specific time slots and frequency sub-carriers known to the transmitter and the receiver. The channel at these pilot time slots and frequency sub-carriers may be estimated using pilot-assisted channel estimation techniques such as zero-forcing, minimum mean square error (MMSE), etc. The channel must also be estimated for the data transmitted at time slots and sub-carriers that are different from those on which pilots are sent. Channel estimation for the data may be determined using prediction methods like linear interpolation and MMSE interpolation.
Even though it is relatively easy to implement, linear interpolation often gives poor results in a frequency selective time-varying environment. In other words, between two points where the channel is estimated based on received pilot signals, the channel may change significantly (not uncommon in mobile radio environments). As a result, the interpolated channel estimates between the two pilots can be quite different from the actual channel at those points. Another drawback is a large mismatch in OFDM between the estimated channels and the true channels at the borders of the time-frequency grid.
Linear MMSE interpolation is based on a model that determines the variation of the channel in time and frequency. For example, the time variation in many cases follows the Jakes model (a model for Rayleigh fading based on summing sinusoids), and the frequency response can be determined using the power delay profile. The linear MMSE interpolation method may be quite satisfactory if the correct model is selected. But if there is a model mismatch, performance suffers. Another drawback of this linear MMSE interpolation is large memory requirements and computational complexity.